diff --git a/pageserver/src/tenant/tasks.rs b/pageserver/src/tenant/tasks.rs
index 00c8ced68a..a845456181 100644
--- a/pageserver/src/tenant/tasks.rs
+++ b/pageserver/src/tenant/tasks.rs
@@ -159,11 +159,8 @@ async fn compaction_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
 
             // TODO: we shouldn't need to await to find tenant and this could be moved outside of
             // loop, #3501. There are also additional "allowed_errors" in tests.
-            if first {
-                first = false;
-                if random_init_delay(period, &cancel).await.is_err() {
-                    break;
-                }
+            if first && random_init_delay(period, &cancel).await.is_err() {
+                break;
             }
 
             let started_at = Instant::now();
@@ -183,7 +180,16 @@ async fn compaction_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
                 }
             };
 
-            warn_when_period_overrun(started_at.elapsed(), period, BackgroundLoopKind::Compaction);
+            if !first {
+                // The first iteration is typically much slower, because all tenants compete for the
+                // compaction sempahore to run, and because of concurrent startup work like initializing
+                // logical sizes.  To avoid routinely spamming warnings, we suppress this log on first iteration.
+                warn_when_period_overrun(
+                    started_at.elapsed(),
+                    period,
+                    BackgroundLoopKind::Compaction,
+                );
+            }
 
             // Sleep
             if tokio::time::timeout(sleep_duration, cancel.cancelled())
@@ -192,6 +198,8 @@ async fn compaction_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
             {
                 break;
             }
+
+            first = false;
         }
     }
     .await;
@@ -223,11 +231,8 @@ async fn gc_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
 
             let period = tenant.get_gc_period();
 
-            if first {
-                first = false;
-                if random_init_delay(period, &cancel).await.is_err() {
-                    break;
-                }
+            if first && random_init_delay(period, &cancel).await.is_err() {
+                break;
             }
 
             let started_at = Instant::now();
@@ -251,7 +256,12 @@ async fn gc_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
                 }
             };
 
-            warn_when_period_overrun(started_at.elapsed(), period, BackgroundLoopKind::Gc);
+            if !first {
+                // The first iteration is typically much slower, because all tenants compete for the
+                // compaction sempahore to run, and because of concurrent startup work like initializing
+                // logical sizes.  To avoid routinely spamming warnings, we suppress this log on first iteration.
+                warn_when_period_overrun(started_at.elapsed(), period, BackgroundLoopKind::Gc);
+            }
 
             // Sleep
             if tokio::time::timeout(sleep_duration, cancel.cancelled())
@@ -260,6 +270,8 @@ async fn gc_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
             {
                 break;
             }
+
+            first = false;
         }
     }
     .await;
diff --git a/pageserver/src/tenant/timeline/walreceiver/connection_manager.rs b/pageserver/src/tenant/timeline/walreceiver/connection_manager.rs
index 36960c631c..e28c4a5f69 100644
--- a/pageserver/src/tenant/timeline/walreceiver/connection_manager.rs
+++ b/pageserver/src/tenant/timeline/walreceiver/connection_manager.rs
@@ -26,8 +26,7 @@ use storage_broker::proto::subscribe_safekeeper_info_request::SubscriptionKey;
 use storage_broker::proto::SafekeeperTimelineInfo;
 use storage_broker::proto::SubscribeSafekeeperInfoRequest;
 use storage_broker::proto::TenantTimelineId as ProtoTenantTimelineId;
-use storage_broker::BrokerClientChannel;
-use storage_broker::Streaming;
+use storage_broker::{BrokerClientChannel, Code, Streaming};
 use tokio::select;
 use tracing::*;
 
@@ -137,8 +136,17 @@ pub(super) async fn connection_manager_loop_step(
             broker_update = broker_subscription.message() => {
                 match broker_update {
                     Ok(Some(broker_update)) => connection_manager_state.register_timeline_update(broker_update),
-                    Err(e) => {
-                        error!("broker subscription failed: {e}");
+                    Err(status) => {
+                        match status.code() {
+                            Code::Unknown if status.message().contains("stream closed because of a broken pipe") => {
+                                // tonic's error handling doesn't provide a clear code for disconnections: we get
+                                // "h2 protocol error: error reading a body from connection: stream closed because of a broken pipe"
+                                info!("broker disconnected: {status}");
+                            },
+                            _ => {
+                                warn!("broker subscription failed: {status}");
+                            }
+                        }
                         return ControlFlow::Continue(());
                     }
                     Ok(None) => {
diff --git a/storage_broker/src/lib.rs b/storage_broker/src/lib.rs
index 3f6fa35cbe..aa5d0bad5f 100644
--- a/storage_broker/src/lib.rs
+++ b/storage_broker/src/lib.rs
@@ -4,7 +4,7 @@ use std::task::{Context, Poll};
 use std::time::Duration;
 use tonic::codegen::StdError;
 use tonic::transport::{ClientTlsConfig, Endpoint};
-use tonic::{transport::Channel, Code, Status};
+use tonic::{transport::Channel, Status};
 use utils::id::{TenantId, TenantTimelineId, TimelineId};
 
 use proto::{
@@ -23,6 +23,7 @@ pub mod proto {
 pub mod metrics;
 
 // Re-exports to avoid direct tonic dependency in user crates.
+pub use tonic::Code;
 pub use tonic::Request;
 pub use tonic::Streaming;